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Linda and Angela contract to paint a neighbor's house. Even

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by BTGmoderatorDC » Tue Aug 21, 2018 2:47 pm
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Linda and Angela contract to paint a neighbor's house. Even though Linda spends 50% more time painting the house than Angela, each receives a payment of m dollars when the work is completed. If Angela decides to pay Linda n dollars so that they would have received the same compensation per hour worked, what is n in terms of m ?

A) 1/2 m
B) 1/3 m
C) 1/4 m
D) 1/5 m
E) 1/6 m

OA D

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by regor60 » Thu Aug 23, 2018 5:47 am
BTGmoderatorDC wrote:Linda and Angela contract to paint a neighbor's house. Even though Linda spends 50% more time painting the house than Angela, each receives a payment of m dollars when the work is completed. If Angela decides to pay Linda n dollars so that they would have received the same compensation per hour worked, what is n in terms of m ?

A) 1/2 m
B) 1/3 m
C) 1/4 m
D) 1/5 m
E) 1/6 m

OA D

Source: Manhattan Prep
Call the amount of time Angela spent T. Therefore the amount of time Linda spent is 1.5T

So Angela's compensation per hour is m/T and Linda's is m/1.5T.

Angela is giving n of her compensation to Linda so that they both have the same per hour compensation. So,

(m+n)/1.5T = (m-n)/T

Cross multiplying: (m+n)/(m-n) = 1.5. Cross multiplying again:

1.5m -1.5n = m+n

Therefore .5m = 2.5n and n=[spoiler] .5m/2.5 = m/5, D[/spoiler]
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by GMATGuruNY » Thu Aug 23, 2018 6:44 am
BTGmoderatorDC wrote:Linda and Angela contract to paint a neighbor's house. Even though Linda spends 50% more time painting the house than Angela, each receives a payment of m dollars when the work is completed. If Angela decides to pay Linda n dollars so that they would have received the same compensation per hour worked, what is n in terms of m ?

A) 1/2 m
B) 1/3 m
C) 1/4 m
D) 1/5 m
E) 1/6 m
Let the pay rate = $1 per hour.

Let Angela's time = 4 hours.
Since Linda works 50% longer, Linda's time = 4 + (1/2)4 = 6 hours.
Since a total of 10 hours are worked at a rate of $1 per hour, the total pay = 10*1 = $10.

Since each worker receives m dollars of the total pay, m=$5.
Since Linda works 6 hours, Angela must give Linda n=$1 so that Linda earns a total of $6 for her 6 hours of work.

The question stem asks for the value of n: $1
Now plug m=5 into the answers to see which yields the target value of $1.
Only D works:
(1/5)m = (1/5)(5) = 1.

The correct answer is D.
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by swerve » Thu Aug 23, 2018 10:55 am
I don't know where I went wrong,

Let say Angela took 2T hours and Linda took 3T hours and each receive m$.

Now, per hour Linda took m/3T and Angela took m/2T.

As given
M/2T-n=M/37+n

I did solve this equation but did not reach the answer.
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by Scott@TargetTestPrep » Thu Aug 23, 2018 4:11 pm
BTGmoderatorDC wrote:Linda and Angela contract to paint a neighbor's house. Even though Linda spends 50% more time painting the house than Angela, each receives a payment of m dollars when the work is completed. If Angela decides to pay Linda n dollars so that they would have received the same compensation per hour worked, what is n in terms of m ?

A) 1/2 m
B) 1/3 m
C) 1/4 m
D) 1/5 m
E) 1/6 m
We can let t = the amount of time Angela worked and create the equation:

(m - n)/t = (m + n)/1.5t

1.5t(m - n) = t(m + n)

1.5(m - n) = (m + n)

1.5m - 1.5n = m + n

0.5m = 2.5n

5m = 25n

5m/25 = n

m/5 = n

(1/5)m = n

Alternate Solution:

Let’s assume that Angela worked 10 hours, and, thus, Linda worked 15 hours. After Angela gives n dollars to Linda, we see that Angela has (m - n) dollars, and Linda has (m + n) dollars. Since this exchange of dollars makes the hourly wage of each painter equal, we have:

Angela’s hourly wage = Linda’s hourly wage

(m - n)/10 = (m + n)/15

15m - 15n = 10m + 10n

5m = 25n

m/5 = n

(1/5)m = n

Answer: D

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